The Cauchy integral, bounded and compact commutators

Ji Li; Trang T. T. Nguyen; Lesley A. Ward; Brett D. Wick

doi:10.4064/sm180715-13-12

The Cauchy integral, bounded and compact commutators

Ji Li, Trang T. T. Nguyen, Lesley A. Ward, Brett D. Wick

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

Abstract

We study the commutator of the well-known Cauchy integral with a locally integrable function b on R, and establish a characterisation of the BMO space on R via the L^p boundedness of this commutator. Moreover, we also establish a characterisation of the VMO space on R via the compactness of this commutator.

Original language	English
Pages (from-to)	193-216
Number of pages	24
Journal	Studia Mathematica
Volume	250
Issue number	2
DOIs	https://doi.org/10.4064/sm180715-13-12
Publication status	Published - 2020

Keywords

BMO spaces
VMO spaces
commutators
Cauchy integrals

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10.4064/sm180715-13-12

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title = "The Cauchy integral, bounded and compact commutators",

abstract = "We study the commutator of the well-known Cauchy integral with a locally integrable function b on R, and establish a characterisation of the BMO space on R via the Lp boundedness of this commutator. Moreover, we also establish a characterisation of the VMO space on R via the compactness of this commutator.",

keywords = "BMO spaces, VMO spaces, commutators, Cauchy integrals",

author = "Ji Li and Nguyen, \{Trang T. T.\} and Ward, \{Lesley A.\} and Wick, \{Brett D.\}",

year = "2020",

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language = "English",

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pages = "193--216",

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TY - JOUR

T1 - The Cauchy integral, bounded and compact commutators

AU - Li, Ji

AU - Nguyen, Trang T. T.

AU - Ward, Lesley A.

AU - Wick, Brett D.

PY - 2020

Y1 - 2020

N2 - We study the commutator of the well-known Cauchy integral with a locally integrable function b on R, and establish a characterisation of the BMO space on R via the Lp boundedness of this commutator. Moreover, we also establish a characterisation of the VMO space on R via the compactness of this commutator.

AB - We study the commutator of the well-known Cauchy integral with a locally integrable function b on R, and establish a characterisation of the BMO space on R via the Lp boundedness of this commutator. Moreover, we also establish a characterisation of the VMO space on R via the compactness of this commutator.

KW - BMO spaces

KW - VMO spaces

KW - commutators

KW - Cauchy integrals

UR - https://www.scopus.com/pages/publications/85075168836

U2 - 10.4064/sm180715-13-12

DO - 10.4064/sm180715-13-12

M3 - Article

SN - 0039-3223

VL - 250

SP - 193

EP - 216

JO - Studia Mathematica

JF - Studia Mathematica

IS - 2

ER -

The Cauchy integral, bounded and compact commutators

Abstract

Keywords

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